Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 704, 7548 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 704, 7548 is 4 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 704, 7548 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 704, 7548 is 4.
HCF(704, 7548) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 704, 7548 is 4.
Step 1: Since 7548 > 704, we apply the division lemma to 7548 and 704, to get
7548 = 704 x 10 + 508
Step 2: Since the reminder 704 ≠ 0, we apply division lemma to 508 and 704, to get
704 = 508 x 1 + 196
Step 3: We consider the new divisor 508 and the new remainder 196, and apply the division lemma to get
508 = 196 x 2 + 116
We consider the new divisor 196 and the new remainder 116,and apply the division lemma to get
196 = 116 x 1 + 80
We consider the new divisor 116 and the new remainder 80,and apply the division lemma to get
116 = 80 x 1 + 36
We consider the new divisor 80 and the new remainder 36,and apply the division lemma to get
80 = 36 x 2 + 8
We consider the new divisor 36 and the new remainder 8,and apply the division lemma to get
36 = 8 x 4 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 704 and 7548 is 4
Notice that 4 = HCF(8,4) = HCF(36,8) = HCF(80,36) = HCF(116,80) = HCF(196,116) = HCF(508,196) = HCF(704,508) = HCF(7548,704) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 704, 7548?
Answer: HCF of 704, 7548 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 704, 7548 using Euclid's Algorithm?
Answer: For arbitrary numbers 704, 7548 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.